Question

algebra 2 mp3 - 6 week test review

1. $\frac{x - 1}{15x + 12}+\frac{8 - 2x}{15x + 12}$

a) $\frac{3x+7}{15x+12}$ b) $\frac{-x+7}{15x+12}$
c) $\frac{8x-8}{15x+12}$ d) $\frac{-x-1}{15x+12}$

1. simplify your answer completely

$\frac{x - 4}{x^2 - 2x - 8}+\frac{x + 8}{x^2 - 2x - 8}$

1. what is the horizontal asymptote of the function below?

$f(x)=\frac{6x - 5}{x^2 - 16x - 70}$
a. $x = 0$
b. no horizontal asymptote
c. $y = 6$
d. $y = 0$

1. find the simplest form.

$\frac{x^2 - 7x - 8}{x^2 - 14x + 48}$
a. $\frac{x+1}{x-6}$ c. $\frac{5x+6}{5x+1}$
b. $\frac{x-6}{x+1}$ d. $\frac{x-4}{x+6}$

1. find the hole of the following rational expression.

$f(x)=\frac{x^2-2x-8}{4x+8}$
a. $(1, -0.75)$
b. $(-1, -1.25)$
c. $(-2, -1.5)$
$(-1, 1.25)$

1. what is the domain of the following rational expression?

$\frac{(x - 8)}{(x - 8)(x + 3)}$
$x\
eq$ _______________

Explanation:

Step1: Add numerators (same denominator)

$\frac{(x-1)+(8-2x)}{15x+12}$

Step2: Combine like terms

$\frac{x-1+8-2x}{15x+12} = \frac{-x+7}{15x+12}$

Step1: Add numerators (same denominator)

$\frac{(x-4)+(x+8)}{x^2-2x-8}$

Step2: Combine like terms

$\frac{x-4+x+8}{x^2-2x-8} = \frac{2x+4}{x^2-2x-8}$

Step3: Factor numerator and denominator

$\frac{2(x+2)}{(x-4)(x+2)}$

Step4: Cancel common factors ($x

eq -2$)
$\frac{2}{x-4}$

Step1: Compare degrees of numerator/denominator

Degree of numerator (1) < Degree of denominator (2)

Step2: Apply horizontal asymptote rule

For $\text{deg}(num) < \text{deg}(denom)$, horizontal asymptote is $y=0$

Step1: Factor numerator and denominator

$\frac{(x-8)(x+1)}{(x-8)(x-6)}$

Step2: Cancel common factors ($x

eq 8$)
$\frac{x+1}{x-6}$

Answer:

B) $\frac{-x+7}{15x+12}$

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